Canadian Geophysical Union abstract

"Integral Equation Techniques Applied to Grid Construction in Acoustic Diffraction Modelling", presented at the 1991 CGU (Canadian Geophysical Union) Annual Meeting in Banff.

We use techniques usually associated with data inversion to analyse a Fredholm integral equation of the first kind for the forward modelling of acoustic scattering by a 2-D body with Dirichlet boundary conditions. The `data' are the incident field values on the body, the unknown `model' is the derivative of the total field on the surface, and there is a a singular Hankel function kernel. We compute the inner product matrix elements and invert to get the surface field derivative, which matches the classical solution for the simple case of the circular cylinder. Grid resolution and node placement requirements are investigated via standard inverse theory approaches, including:

  1. an averaging function analysis,
  2. a chi-squared analysis for both coarse and fine grids and
  3. a spatial weighting function analysis.
The work is not meant to speed up computation of complicated models but to provide some rules for designing grids for both standard and adaptive or multigrid numerical methods.